I think you pretty much "inherit" a particular decompression algorithm when you buy your dive computer. Different manufacturers use different algorithms. Since there aren't any agreed upon standards, its pretty much up to software programs and the dive computer manufacturer's decisions on algorithms. As usual, if you have a preference, caveat emptor.
This 2018 study compares algorithms and might answer so9me of your questions:
Whilst the US Navy has been very systematic about validating Navy dive computer algorithms, there has been little documented or published evidence of rigorous testing of the algorithms in commercial off-the-shelf dive computers. This paper reports ...
pmc.ncbi.nlm.nih.gov
If you use tables instead of a computer, you inherit the algorithms used to develop the tables. NOAA, PADI, NAUI, CMAS
It seems to me that a great deal of the discusion is driven by the technical diving, deep and planned decompression diving community which has gone to Buhlmann because you can tailor or optimise the model's gradient factors to fit your planned dive profile.
The average recreational divers I see here in Bonaire basically set their computer's O2 fraction, O2 pp limit, decide if they want to use conservative settings, follow their dive computers and stick to NDL's. Their understanding of which algorithm, gradient factors, RGBM, etc just isn't there. Dive computers have made it pretty much "monkey-bannana" for recreational NDL divers.
here's some reading material on where the USN and the Swedish military are. As usual, the USN used a different algorythm, tested with actual divers, and used empirical data to derive their latest tables.
https://apps.dtic.mil/sti/pdfs/ADA561928.pdf